Question

so here's the proof of 0=1 if someone not checked i proved 1=2 he can check that out i just worked to form lets see now.
Prove:0=1.
proof: LHS =0= 0+0+0.....
= 1-1+1-1+1-1+1-1........
=(1-1)+(1-1)+(1-1)...........
= 1(-1+1)+(-1+1)+(-1+1).....
=1+0+0+0+0
=>1
hence proved 0=1
want more like this then comment however i m leaving last message for u guys.^_^​

Answer 1

Answer:

No, the actual problem is that the convergence of an infinite series has not been properly defined in this problem. Given epsilon>0, -1+1-1+1-1+1-1+1-... cannot be defined since the difference between the sum of the series and the supposed 'limit' is not less than epsilon for all n>N, N being any arbitrarily large number. (The series diverges by bounded oscillation.) Therefore, supposing that 0=1-1+1-1+1-1+1-1... is wrong